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游游 · 2024年10月12日

借钱的组合

NO.PZ2023091901000026

问题如下:

The market portfolio (M) contains the optimal allocation of only risky asset and no risky assets. Let the S1 be the Sharpe ratio of this market portfolio. There exists a risk-free asset. Initially, an investor is fully (100%) invested in M with a portfolio Sharpe ratio of S1. Subsequently, the investor borrows 30% at the risk-free rate, such that she is 130% invested in the market portfolio (M) where this leverage portfolio has a Sharpe ratio of S2。After the leverage (i.e., borrowing at the risk-free rate to invest +30% in M, is the investor still on the efficient frontier and how do the Sharpe ratios?

选项:

A.

No (no longer efficient), and S2

B.

No, but S2 = S1.

C.

Yes (still efficient), but S2

D.

Yes and S2 = S1.

解释:

The ability to borrowing or lend morphs the concave/convex efficient frontier into the linear CML; i.e., the leveraged portfolio is efficient with higher risk and higher return.

All portfolios on the CML have the same Sharpe ratio: the slope of the CML.


借用或借出的能力将凹/凸有效边界变为线性CML;
也就是说,杠杆投资组合具有较高的风险和较高的收益。
CML上的所有投资组合都有相同的夏普比率:CML的斜率。

有效前沿线不是那条曲线吗?借钱的组合不是在CML上,那个线没在EL上了啊?

1 个答案
已采纳答案

pzqa27 · 2024年10月12日

嗨,爱思考的PZer你好:


你提到的有效前沿线通常指仅包含风险资产的情形。在没有无风险资产时,组合只能在曲线(有效前沿)上进行选择。但在有无风险资产并允许借贷的情况下,所有投资组合将沿着CML移动,市场组合(M)是其中的一个特殊点(在100%投资时)。借贷投资则意味着你进一步沿着CML向右移动,增加风险与回报,依然是有效的投资组合。

因此,借贷后组合不再在曲线状的有效前沿上,但它仍然在线性CML上,并且CML的所有组合都具有相同的夏普比率。

----------------------------------------------
就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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